⑩天掌 Teaching Plan on Advanced Mathematics o (2)当周期为2m的偶函数∫(x)展开成傅里叶级数时,它的傅 里叶系数为 广:(x)oso(m=012) b.=0 (n=1,2,…) 证明(1)设f(x)是奇函数, ∫f( x)cos nx x=0( n=0,1,2,3,) 奇函数 tianjin polytechnic dmivendityTianjin Polytechnic University Teaching Plan on Advanced Mathematics (2)当周期为2 的偶函数 f (x)展开成傅里叶级数时,它的傅 里叶系数为 0 ( 1,2, ) ( )cos ( 0,1,2, ) 2 0   = = =  =   b n a f x nxdx n n n 证明 (1)设f (x)是奇函数,   =  − an f (x)cos nxdx 1 = 0 (n = 0,1,2,3, ) 奇函数